Portrait of Ian Hornik wearing glasses, a blue suit and blue tie with white square, standing in front of a stone wall with halfround windows.

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Name: Ian HORNIK
Current position: Master student Technical Mathematics and student assistant in teaching
Topic of diploma thesis: The Drury–Arveson space
Supervisor: Prof. Harald WORACEK

In my thesis I construct a multivariable generalization of the Hardy–Hilbert space, namely the Drury–Arveson space. Using methods from complex function theory and functional analysis, a rich theory emerges. First, this space can be described in several ways: as a space of formal power series, as the coisometric image of a space of noncommutative power series, as a function-theoretic space, and as a reproducing kernel Hilbert space. The interplay of these descriptions makes it possible, for example, to classify interpolation problems in which certain nodes are to be interpolated to data points by means of an analytic function.

The focus of my work lies in the formal development of the already existing theory of the space. My area of interest clearly lies in complex function theory and functional analysis, and I therefore hope to be able to continue studying similarly exciting objects in the future.

Further information: CV, opens an external URL in a new window, website, opens an external URL in a new window